A friend of mine owns one and said that you are supposed to store it hanging up, with the valve open to keep the lifetime warranty. Is that correct?

I've always stored mine by opening the valve all the way & folding it in half. This allows the foam core to retain it's original size & self-inflate much faster.

No. This is the best way to store the pad if you want optimum performance (meaning if you want it to inflate super fast), but storing it rolled up will not void the warranty. There are other things that will void it like leaving it in a hot car, putting hot items like pots of boiling water on it, using it to ward of a bear attack, using it to slide down a scree slope, etc., but leaving it rolled up is not one of these. FYI, If you do have it rolled up for an extended period of time and want to 'revive' it, simply blow as much air into it as you can and leave it overnight. This will help the foam regain it's lost memory and allow it to inflate at it's fasted rate. Unlike popular myths, Thermarest mattresses won't lose their self-inflating capabilities by storing them rolled up. They are not like sleeping bags that if left stuffed in small stuff sacks will lose their loft. Thermarest self-inflatable mattresses can be revived...